ABSTRACT
This chapter presents topics and notations that are needed in this book. Part of the results are of interests themselves. Some are not included in the standard introductory graduate texts of complex analysis. The chapter deals with the convergence of the family of meromorphic functions. As a quantitative generalization of Picard’s theorem, the theory of the distribution of values of meromorphic functions, developed by R. Nevanlinna and then L. Ahlfors was one of the most outstanding achievements of mathematics in this century. The chapter presents a brief account of Nevanlinna’s value distribution theory. A more geometric approach to value distribution theory was introduced by Ahlfors in 1935, which has proved powerful tool in its own right and has led to such new insights as the connection with geometric analysis. The Wiman-Valiron theory is important in the study of value distribution theory and its applications such as the growth estimates of solutions of differential equations in the complex domain.
